library(readr)
## Warning: package 'readr' was built under R version 3.5.2
library(knitr)
library(caret)
## Warning: package 'caret' was built under R version 3.5.3
## Loading required package: lattice
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 3.5.2
housing_data = read_csv("housing.csv")#first line of housing
## Parsed with column specification:
## cols(
## longitude = col_double(),
## latitude = col_double(),
## housing_median_age = col_double(),
## total_rooms = col_double(),
## total_bedrooms = col_double(),
## population = col_double(),
## households = col_double(),
## median_income = col_double(),
## median_house_value = col_double(),
## ocean_proximity = col_character()
## )
housing_data$median_house_value[1:100]
## [1] 452600 358500 352100 341300 342200 269700 299200 241400 226700 261100
## [11] 281500 241800 213500 191300 159200 140000 152500 155500 158700 162900
## [21] 147500 159800 113900 99700 132600 107500 93800 105500 108900 132000
## [31] 122300 115200 110400 104900 109700 97200 104500 103900 191400 176000
## [41] 155400 150000 118800 188800 184400 182300 142500 137500 187500 112500
## [51] 171900 93800 97500 104200 87500 83100 87500 85300 80300 60000
## [61] 75700 75000 86100 76100 73500 78400 84400 81300 85000 129200
## [71] 82500 95200 75000 67500 137500 177500 102100 108300 112500 131300
## [81] 162500 112500 112500 137500 118800 98200 118800 162500 137500 500001
## [91] 162500 137500 162500 187500 179200 130000 183800 125000 170000 193100
summary(housing_data)#gives us a summary of each column. Note that total bedrooms has 207 NA's. We will need to impute these values
## longitude latitude housing_median_age total_rooms
## Min. :-124.3 Min. :32.54 Min. : 1.00 Min. : 2
## 1st Qu.:-121.8 1st Qu.:33.93 1st Qu.:18.00 1st Qu.: 1448
## Median :-118.5 Median :34.26 Median :29.00 Median : 2127
## Mean :-119.6 Mean :35.63 Mean :28.64 Mean : 2636
## 3rd Qu.:-118.0 3rd Qu.:37.71 3rd Qu.:37.00 3rd Qu.: 3148
## Max. :-114.3 Max. :41.95 Max. :52.00 Max. :39320
##
## total_bedrooms population households median_income
## Min. : 1.0 Min. : 3 Min. : 1.0 Min. : 0.4999
## 1st Qu.: 296.0 1st Qu.: 787 1st Qu.: 280.0 1st Qu.: 2.5634
## Median : 435.0 Median : 1166 Median : 409.0 Median : 3.5348
## Mean : 537.9 Mean : 1425 Mean : 499.5 Mean : 3.8707
## 3rd Qu.: 647.0 3rd Qu.: 1725 3rd Qu.: 605.0 3rd Qu.: 4.7432
## Max. :6445.0 Max. :35682 Max. :6082.0 Max. :15.0001
## NA's :207
## median_house_value ocean_proximity
## Min. : 14999 Length:20640
## 1st Qu.:119600 Class :character
## Median :179700 Mode :character
## Mean :206856
## 3rd Qu.:264725
## Max. :500001
##
library(ggplot2)
#we want to look at shape of distribution to get a good idea of what to impute
ggplot(housing_data, aes(x = total_bedrooms)) +
geom_histogram(bins = 40) +
xlab("Total Bedrooms") +
ylab("Density") +
ggtitle("Histogram of Total Bedrooms (noncontinuous variable)")
## Warning: Removed 207 rows containing non-finite values (stat_bin).
#using mean for now
library(mice)
## Warning: package 'mice' was built under R version 3.5.3
##
## Attaching package: 'mice'
## The following objects are masked from 'package:base':
##
## cbind, rbind
housing_data_temp = mice(data = housing_data, m = 5, method = "mean", seed = 420)
##
## iter imp variable
## 1 1 total_bedrooms
## 1 2 total_bedrooms
## 1 3 total_bedrooms
## 1 4 total_bedrooms
## 1 5 total_bedrooms
## 2 1 total_bedrooms
## 2 2 total_bedrooms
## 2 3 total_bedrooms
## 2 4 total_bedrooms
## 2 5 total_bedrooms
## 3 1 total_bedrooms
## 3 2 total_bedrooms
## 3 3 total_bedrooms
## 3 4 total_bedrooms
## 3 5 total_bedrooms
## 4 1 total_bedrooms
## 4 2 total_bedrooms
## 4 3 total_bedrooms
## 4 4 total_bedrooms
## 4 5 total_bedrooms
## 5 1 total_bedrooms
## 5 2 total_bedrooms
## 5 3 total_bedrooms
## 5 4 total_bedrooms
## 5 5 total_bedrooms
## Warning: Number of logged events: 1
housing_data_full = complete(housing_data_temp, 1)
housing_data_full$ocean_proximity = as.factor(housing_data_full$ocean_proximity)
housing_data_nc = housing_data_full[, -10]#remove text variable for now
corrmatrix = cor(housing_data_nc)
kable(t(corrmatrix))
| longitude |
1.0000000 |
-0.9246644 |
-0.1081968 |
0.0445680 |
0.0692597 |
0.0997732 |
0.0553101 |
-0.0151759 |
-0.0459666 |
| latitude |
-0.9246644 |
1.0000000 |
0.0111727 |
-0.0360996 |
-0.0666584 |
-0.1087847 |
-0.0710354 |
-0.0798091 |
-0.1441603 |
| housing_median_age |
-0.1081968 |
0.0111727 |
1.0000000 |
-0.3612622 |
-0.3189983 |
-0.2962442 |
-0.3029160 |
-0.1190340 |
0.1056234 |
| total_rooms |
0.0445680 |
-0.0360996 |
-0.3612622 |
1.0000000 |
0.9272527 |
0.8571260 |
0.9184845 |
0.1980496 |
0.1341531 |
| total_bedrooms |
0.0692597 |
-0.0666584 |
-0.3189983 |
0.9272527 |
1.0000000 |
0.8739095 |
0.9747249 |
-0.0076819 |
0.0494535 |
| population |
0.0997732 |
-0.1087847 |
-0.2962442 |
0.8571260 |
0.8739095 |
1.0000000 |
0.9072223 |
0.0048343 |
-0.0246497 |
| households |
0.0553101 |
-0.0710354 |
-0.3029160 |
0.9184845 |
0.9747249 |
0.9072223 |
1.0000000 |
0.0130331 |
0.0658427 |
| median_income |
-0.0151759 |
-0.0798091 |
-0.1190340 |
0.1980496 |
-0.0076819 |
0.0048343 |
0.0130331 |
1.0000000 |
0.6880752 |
| median_house_value |
-0.0459666 |
-0.1441603 |
0.1056234 |
0.1341531 |
0.0494535 |
-0.0246497 |
0.0658427 |
0.6880752 |
1.0000000 |
highcorr = findCorrelation(corrmatrix, cutoff = .60)#this will give you highly correlated variables
library(scales)
## Warning: package 'scales' was built under R version 3.5.3
##
## Attaching package: 'scales'
## The following object is masked from 'package:readr':
##
## col_factor
library(RColorBrewer)
## Warning: package 'RColorBrewer' was built under R version 3.5.2
library(plotly)
## Warning: package 'plotly' was built under R version 3.5.3
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
plot_map = ggplot(housing_data_full,
aes(x = longitude, y = latitude, color = median_house_value, hma = housing_median_age,
tr = total_rooms, tb = total_bedrooms, hh = households, mi = median_income)) +
geom_point(aes(size = population), alpha = 0.4) +
xlab("Longitude") +
ylab("Latitude") +
ggtitle("Data Map - Longtitude vs Latitude and Associated Variables") +
theme(plot.title = element_text(hjust = 0.5)) +
scale_color_distiller(palette = "Paired", labels = comma) +
labs(color = "Median House Value (in $USD)", size = "Population")
plot_map_tt = ggplotly(plot_map)
plot_map_tt
temp_housing_data = housing_data_full[housing_data_full$ocean_proximity != "ISLAND", ] #possibly consider removing #ISLAND promiximity homes. There are 5 in the dataset out of 20k observations.
start_mod = lm(median_house_value ~ (.)^2, data = temp_housing_data)
n = length(resid(start_mod))
back_bic_mod = step(start_mod, direction = "backward", k = log(n))
## Start: AIC=456726.7
## median_house_value ~ (longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity)^2
##
## Df Sum of Sq RSS AIC
## - total_bedrooms:ocean_proximity 3 3.3966e+10 8.2016e+13 456705
## - total_rooms:total_bedrooms 1 9.1245e+07 8.1982e+13 456717
## - housing_median_age:total_bedrooms 1 9.9335e+08 8.1983e+13 456717
## - households:ocean_proximity 3 8.0876e+10 8.2063e+13 456717
## - total_bedrooms:median_income 1 2.3709e+09 8.1985e+13 456717
## - longitude:households 1 1.8557e+10 8.2001e+13 456721
## - total_bedrooms:population 1 2.3950e+10 8.2006e+13 456723
## - latitude:households 1 2.6834e+10 8.2009e+13 456723
## - longitude:population 1 2.7677e+10 8.2010e+13 456724
## <none> 8.1982e+13 456727
## - households:median_income 1 4.3377e+10 8.2026e+13 456728
## - latitude:population 1 5.3803e+10 8.2036e+13 456730
## - longitude:total_bedrooms 1 6.1010e+10 8.2043e+13 456732
## - population:median_income 1 6.4331e+10 8.2047e+13 456733
## - total_rooms:ocean_proximity 3 1.4739e+11 8.2130e+13 456734
## - housing_median_age:total_rooms 1 7.6819e+10 8.2059e+13 456736
## - housing_median_age:median_income 1 8.7309e+10 8.2070e+13 456739
## - total_rooms:households 1 9.1399e+10 8.2074e+13 456740
## - population:households 1 9.2161e+10 8.2074e+13 456740
## - latitude:total_bedrooms 1 9.8267e+10 8.2080e+13 456741
## - housing_median_age:ocean_proximity 3 1.8076e+11 8.2163e+13 456742
## - longitude:total_rooms 1 1.2431e+11 8.2107e+13 456748
## - total_rooms:median_income 1 1.3340e+11 8.2116e+13 456750
## - latitude:total_rooms 1 1.5767e+11 8.2140e+13 456756
## - total_rooms:population 1 1.8232e+11 8.2165e+13 456763
## - median_income:ocean_proximity 3 3.1068e+11 8.2293e+13 456775
## - population:ocean_proximity 3 3.8433e+11 8.2367e+13 456793
## - longitude:latitude 1 3.9347e+11 8.2376e+13 456816
## - total_bedrooms:households 1 3.9597e+11 8.2378e+13 456816
## - housing_median_age:households 1 4.2291e+11 8.2405e+13 456823
## - longitude:housing_median_age 1 4.5976e+11 8.2442e+13 456832
## - latitude:housing_median_age 1 6.3099e+11 8.2613e+13 456875
## - longitude:median_income 1 6.5260e+11 8.2635e+13 456880
## - latitude:median_income 1 7.2664e+11 8.2709e+13 456899
## - housing_median_age:population 1 9.7874e+11 8.2961e+13 456962
## - latitude:ocean_proximity 3 1.2166e+12 8.3199e+13 457001
## - longitude:ocean_proximity 3 2.1565e+12 8.4139e+13 457233
##
## Step: AIC=456705.4
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:population +
## longitude:households + longitude:median_income + longitude:ocean_proximity +
## latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms +
## latitude:population + latitude:households + latitude:median_income +
## latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:total_bedrooms + housing_median_age:population +
## housing_median_age:households + housing_median_age:median_income +
## housing_median_age:ocean_proximity + total_rooms:total_bedrooms +
## total_rooms:population + total_rooms:households + total_rooms:median_income +
## total_rooms:ocean_proximity + total_bedrooms:population +
## total_bedrooms:households + total_bedrooms:median_income +
## population:households + population:median_income + population:ocean_proximity +
## households:median_income + households:ocean_proximity + median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - total_rooms:total_bedrooms 1 1.1063e+09 8.2017e+13 456696
## - housing_median_age:total_bedrooms 1 2.1540e+09 8.2018e+13 456696
## - total_bedrooms:median_income 1 2.9676e+09 8.2019e+13 456696
## - households:ocean_proximity 3 8.7377e+10 8.2104e+13 456698
## - total_bedrooms:population 1 1.3989e+10 8.2030e+13 456699
## - longitude:households 1 2.6159e+10 8.2042e+13 456702
## - longitude:population 1 2.7868e+10 8.2044e+13 456702
## - latitude:households 1 3.7451e+10 8.2054e+13 456705
## <none> 8.2016e+13 456705
## - households:median_income 1 4.5228e+10 8.2061e+13 456707
## - latitude:population 1 5.5671e+10 8.2072e+13 456709
## - population:median_income 1 6.4610e+10 8.2081e+13 456712
## - housing_median_age:total_rooms 1 7.3952e+10 8.2090e+13 456714
## - total_rooms:ocean_proximity 3 1.6112e+11 8.2177e+13 456716
## - housing_median_age:median_income 1 8.3276e+10 8.2099e+13 456716
## - total_rooms:households 1 8.8196e+10 8.2104e+13 456718
## - housing_median_age:ocean_proximity 3 1.7426e+11 8.2190e+13 456719
## - longitude:total_bedrooms 1 9.5540e+10 8.2112e+13 456720
## - longitude:total_rooms 1 1.3119e+11 8.2147e+13 456728
## - total_rooms:median_income 1 1.3250e+11 8.2149e+13 456729
## - population:households 1 1.4602e+11 8.2162e+13 456732
## - latitude:total_bedrooms 1 1.5925e+11 8.2175e+13 456736
## - latitude:total_rooms 1 1.7523e+11 8.2191e+13 456740
## - total_rooms:population 1 1.8910e+11 8.2205e+13 456743
## - median_income:ocean_proximity 3 3.0915e+11 8.2325e+13 456753
## - population:ocean_proximity 3 3.6036e+11 8.2377e+13 456766
## - longitude:latitude 1 3.9532e+11 8.2412e+13 456795
## - total_bedrooms:households 1 4.1177e+11 8.2428e+13 456799
## - housing_median_age:households 1 4.5132e+11 8.2468e+13 456809
## - longitude:housing_median_age 1 4.6022e+11 8.2476e+13 456811
## - latitude:housing_median_age 1 6.3264e+11 8.2649e+13 456854
## - longitude:median_income 1 6.8519e+11 8.2701e+13 456867
## - latitude:median_income 1 7.6876e+11 8.2785e+13 456888
## - housing_median_age:population 1 9.8590e+11 8.3002e+13 456942
## - latitude:ocean_proximity 3 1.2232e+12 8.3239e+13 456981
## - longitude:ocean_proximity 3 2.1653e+12 8.4181e+13 457213
##
## Step: AIC=456695.8
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:population +
## longitude:households + longitude:median_income + longitude:ocean_proximity +
## latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms +
## latitude:population + latitude:households + latitude:median_income +
## latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:total_bedrooms + housing_median_age:population +
## housing_median_age:households + housing_median_age:median_income +
## housing_median_age:ocean_proximity + total_rooms:population +
## total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity +
## total_bedrooms:population + total_bedrooms:households + total_bedrooms:median_income +
## population:households + population:median_income + population:ocean_proximity +
## households:median_income + households:ocean_proximity + median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - total_bedrooms:median_income 1 2.5553e+09 8.2020e+13 456686
## - housing_median_age:total_bedrooms 1 3.1234e+09 8.2020e+13 456687
## - households:ocean_proximity 3 8.7733e+10 8.2105e+13 456688
## - total_bedrooms:population 1 2.5262e+10 8.2043e+13 456692
## - longitude:population 1 2.8284e+10 8.2046e+13 456693
## - longitude:households 1 3.1457e+10 8.2049e+13 456694
## <none> 8.2017e+13 456696
## - latitude:households 1 4.0683e+10 8.2058e+13 456696
## - households:median_income 1 4.4212e+10 8.2062e+13 456697
## - latitude:population 1 5.6079e+10 8.2073e+13 456700
## - population:median_income 1 6.5561e+10 8.2083e+13 456702
## - housing_median_age:total_rooms 1 7.4381e+10 8.2092e+13 456705
## - total_rooms:ocean_proximity 3 1.6041e+11 8.2178e+13 456706
## - housing_median_age:median_income 1 8.3430e+10 8.2101e+13 456707
## - housing_median_age:ocean_proximity 3 1.7407e+11 8.2191e+13 456710
## - longitude:total_bedrooms 1 9.5982e+10 8.2113e+13 456710
## - total_rooms:median_income 1 1.3217e+11 8.2149e+13 456719
## - longitude:total_rooms 1 1.3427e+11 8.2152e+13 456720
## - latitude:total_bedrooms 1 1.5834e+11 8.2176e+13 456726
## - total_rooms:households 1 1.7352e+11 8.2191e+13 456729
## - latitude:total_rooms 1 1.7765e+11 8.2195e+13 456730
## - total_rooms:population 1 1.8828e+11 8.2206e+13 456733
## - median_income:ocean_proximity 3 3.0811e+11 8.2325e+13 456743
## - population:households 1 2.5710e+11 8.2274e+13 456750
## - population:ocean_proximity 3 3.5958e+11 8.2377e+13 456756
## - longitude:latitude 1 3.9452e+11 8.2412e+13 456785
## - total_bedrooms:households 1 4.1068e+11 8.2428e+13 456789
## - longitude:housing_median_age 1 4.5931e+11 8.2477e+13 456801
## - housing_median_age:households 1 4.8648e+11 8.2504e+13 456808
## - latitude:housing_median_age 1 6.3165e+11 8.2649e+13 456844
## - longitude:median_income 1 6.8719e+11 8.2704e+13 456858
## - latitude:median_income 1 7.7050e+11 8.2788e+13 456879
## - housing_median_age:population 1 9.8483e+11 8.3002e+13 456932
## - latitude:ocean_proximity 3 1.2224e+12 8.3240e+13 456971
## - longitude:ocean_proximity 3 2.1642e+12 8.4181e+13 457203
##
## Step: AIC=456686.5
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:population +
## longitude:households + longitude:median_income + longitude:ocean_proximity +
## latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms +
## latitude:population + latitude:households + latitude:median_income +
## latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:total_bedrooms + housing_median_age:population +
## housing_median_age:households + housing_median_age:median_income +
## housing_median_age:ocean_proximity + total_rooms:population +
## total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity +
## total_bedrooms:population + total_bedrooms:households + population:households +
## population:median_income + population:ocean_proximity + households:median_income +
## households:ocean_proximity + median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - housing_median_age:total_bedrooms 1 2.0299e+09 8.2022e+13 456677
## - households:ocean_proximity 3 8.7069e+10 8.2107e+13 456679
## - total_bedrooms:population 1 2.7022e+10 8.2047e+13 456683
## - longitude:population 1 2.8545e+10 8.2048e+13 456684
## - longitude:households 1 3.3347e+10 8.2053e+13 456685
## <none> 8.2020e+13 456686
## - latitude:households 1 4.3781e+10 8.2064e+13 456688
## - latitude:population 1 5.6298e+10 8.2076e+13 456691
## - population:median_income 1 6.3082e+10 8.2083e+13 456692
## - housing_median_age:total_rooms 1 7.3394e+10 8.2093e+13 456695
## - households:median_income 1 7.5800e+10 8.2096e+13 456696
## - total_rooms:ocean_proximity 3 1.5887e+11 8.2179e+13 456697
## - housing_median_age:median_income 1 8.3562e+10 8.2103e+13 456698
## - housing_median_age:ocean_proximity 3 1.7339e+11 8.2193e+13 456700
## - longitude:total_bedrooms 1 9.4292e+10 8.2114e+13 456700
## - longitude:total_rooms 1 1.3173e+11 8.2152e+13 456710
## - total_rooms:median_income 1 1.3243e+11 8.2152e+13 456710
## - latitude:total_bedrooms 1 1.5895e+11 8.2179e+13 456716
## - total_rooms:households 1 1.7110e+11 8.2191e+13 456720
## - latitude:total_rooms 1 1.7511e+11 8.2195e+13 456721
## - total_rooms:population 1 1.8608e+11 8.2206e+13 456723
## - median_income:ocean_proximity 3 3.0580e+11 8.2326e+13 456733
## - population:households 1 2.5813e+11 8.2278e+13 456741
## - population:ocean_proximity 3 3.5744e+11 8.2377e+13 456746
## - longitude:latitude 1 3.9378e+11 8.2414e+13 456775
## - total_bedrooms:households 1 4.0815e+11 8.2428e+13 456779
## - longitude:housing_median_age 1 4.6132e+11 8.2481e+13 456792
## - housing_median_age:households 1 4.9580e+11 8.2516e+13 456801
## - latitude:housing_median_age 1 6.3387e+11 8.2654e+13 456835
## - longitude:median_income 1 6.9069e+11 8.2711e+13 456850
## - latitude:median_income 1 7.7281e+11 8.2793e+13 456870
## - housing_median_age:population 1 9.8521e+11 8.3005e+13 456923
## - latitude:ocean_proximity 3 1.2204e+12 8.3240e+13 456961
## - longitude:ocean_proximity 3 2.1626e+12 8.4182e+13 457194
##
## Step: AIC=456677
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:population +
## longitude:households + longitude:median_income + longitude:ocean_proximity +
## latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms +
## latitude:population + latitude:households + latitude:median_income +
## latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:population + housing_median_age:households +
## housing_median_age:median_income + housing_median_age:ocean_proximity +
## total_rooms:population + total_rooms:households + total_rooms:median_income +
## total_rooms:ocean_proximity + total_bedrooms:population +
## total_bedrooms:households + population:households + population:median_income +
## population:ocean_proximity + households:median_income + households:ocean_proximity +
## median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - households:ocean_proximity 3 8.6819e+10 8.2109e+13 456669
## - longitude:population 1 2.8898e+10 8.2051e+13 456674
## - total_bedrooms:population 1 3.2757e+10 8.2055e+13 456675
## - longitude:households 1 3.7782e+10 8.2060e+13 456677
## <none> 8.2022e+13 456677
## - latitude:households 1 4.7102e+10 8.2069e+13 456679
## - latitude:population 1 5.6585e+10 8.2078e+13 456681
## - population:median_income 1 6.5167e+10 8.2087e+13 456684
## - households:median_income 1 7.6714e+10 8.2099e+13 456686
## - total_rooms:ocean_proximity 3 1.5800e+11 8.2180e+13 456687
## - housing_median_age:total_rooms 1 9.0793e+10 8.2113e+13 456690
## - longitude:total_bedrooms 1 9.3476e+10 8.2115e+13 456691
## - housing_median_age:median_income 1 9.4407e+10 8.2116e+13 456691
## - housing_median_age:ocean_proximity 3 1.7542e+11 8.2197e+13 456691
## - longitude:total_rooms 1 1.3060e+11 8.2152e+13 456700
## - total_rooms:median_income 1 1.3267e+11 8.2155e+13 456700
## - latitude:total_bedrooms 1 1.5781e+11 8.2180e+13 456707
## - total_rooms:households 1 1.6984e+11 8.2192e+13 456710
## - latitude:total_rooms 1 1.7370e+11 8.2196e+13 456711
## - total_rooms:population 1 1.8733e+11 8.2209e+13 456714
## - median_income:ocean_proximity 3 3.0455e+11 8.2326e+13 456724
## - population:households 1 2.7241e+11 8.2294e+13 456736
## - population:ocean_proximity 3 3.5668e+11 8.2379e+13 456737
## - longitude:latitude 1 3.9416e+11 8.2416e+13 456766
## - total_bedrooms:households 1 4.0745e+11 8.2429e+13 456769
## - longitude:housing_median_age 1 4.6683e+11 8.2489e+13 456784
## - latitude:housing_median_age 1 6.3894e+11 8.2661e+13 456827
## - longitude:median_income 1 6.8874e+11 8.2711e+13 456840
## - latitude:median_income 1 7.7086e+11 8.2793e+13 456860
## - housing_median_age:population 1 1.0009e+12 8.3023e+13 456917
## - latitude:ocean_proximity 3 1.2208e+12 8.3243e+13 456952
## - housing_median_age:households 1 1.2775e+12 8.3299e+13 456986
## - longitude:ocean_proximity 3 2.1610e+12 8.4183e+13 457184
##
## Step: AIC=456669.1
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:population +
## longitude:households + longitude:median_income + longitude:ocean_proximity +
## latitude:housing_median_age + latitude:total_rooms + latitude:total_bedrooms +
## latitude:population + latitude:households + latitude:median_income +
## latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:population + housing_median_age:households +
## housing_median_age:median_income + housing_median_age:ocean_proximity +
## total_rooms:population + total_rooms:households + total_rooms:median_income +
## total_rooms:ocean_proximity + total_bedrooms:population +
## total_bedrooms:households + population:households + population:median_income +
## population:ocean_proximity + households:median_income + median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - longitude:population 1 1.7928e+10 8.2127e+13 456664
## - longitude:households 1 2.4690e+10 8.2133e+13 456665
## - total_bedrooms:population 1 3.2510e+10 8.2141e+13 456667
## <none> 8.2109e+13 456669
## - latitude:households 1 4.4200e+10 8.2153e+13 456670
## - latitude:population 1 4.8712e+10 8.2157e+13 456671
## - population:median_income 1 7.4432e+10 8.2183e+13 456678
## - longitude:total_bedrooms 1 8.3137e+10 8.2192e+13 456680
## - households:median_income 1 8.7278e+10 8.2196e+13 456681
## - housing_median_age:total_rooms 1 8.8601e+10 8.2197e+13 456681
## - housing_median_age:median_income 1 9.5562e+10 8.2204e+13 456683
## - housing_median_age:ocean_proximity 3 1.8170e+11 8.2290e+13 456685
## - longitude:total_rooms 1 1.2967e+11 8.2238e+13 456692
## - total_rooms:median_income 1 1.3273e+11 8.2241e+13 456692
## - latitude:total_bedrooms 1 1.5242e+11 8.2261e+13 456697
## - total_rooms:households 1 1.6981e+11 8.2279e+13 456702
## - total_rooms:population 1 1.9097e+11 8.2300e+13 456707
## - latitude:total_rooms 1 1.9999e+11 8.2309e+13 456709
## - total_rooms:ocean_proximity 3 2.8796e+11 8.2397e+13 456712
## - population:households 1 2.7898e+11 8.2388e+13 456729
## - population:ocean_proximity 3 4.0867e+11 8.2517e+13 456742
## - median_income:ocean_proximity 3 4.1706e+11 8.2526e+13 456744
## - longitude:latitude 1 3.8852e+11 8.2497e+13 456757
## - total_bedrooms:households 1 4.0019e+11 8.2509e+13 456759
## - longitude:housing_median_age 1 4.7191e+11 8.2581e+13 456777
## - latitude:housing_median_age 1 6.4854e+11 8.2757e+13 456821
## - longitude:median_income 1 6.9310e+11 8.2802e+13 456833
## - latitude:median_income 1 7.9933e+11 8.2908e+13 456859
## - housing_median_age:population 1 1.0055e+12 8.3114e+13 456910
## - latitude:ocean_proximity 3 1.2363e+12 8.3345e+13 456948
## - housing_median_age:households 1 1.3227e+12 8.3431e+13 456989
## - longitude:ocean_proximity 3 2.1824e+12 8.4291e+13 457181
##
## Step: AIC=456663.7
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:households +
## longitude:median_income + longitude:ocean_proximity + latitude:housing_median_age +
## latitude:total_rooms + latitude:total_bedrooms + latitude:population +
## latitude:households + latitude:median_income + latitude:ocean_proximity +
## housing_median_age:total_rooms + housing_median_age:population +
## housing_median_age:households + housing_median_age:median_income +
## housing_median_age:ocean_proximity + total_rooms:population +
## total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity +
## total_bedrooms:population + total_bedrooms:households + population:households +
## population:median_income + population:ocean_proximity + households:median_income +
## median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - longitude:households 1 1.0557e+10 8.2137e+13 456656
## - total_bedrooms:population 1 2.5196e+10 8.2152e+13 456660
## - latitude:households 1 2.6992e+10 8.2154e+13 456660
## <none> 8.2127e+13 456664
## - population:median_income 1 8.2988e+10 8.2210e+13 456675
## - latitude:population 1 8.6665e+10 8.2213e+13 456675
## - housing_median_age:total_rooms 1 9.4969e+10 8.2222e+13 456678
## - households:median_income 1 9.7593e+10 8.2224e+13 456678
## - housing_median_age:median_income 1 1.0014e+11 8.2227e+13 456679
## - housing_median_age:ocean_proximity 3 1.8124e+11 8.2308e+13 456679
## - longitude:total_bedrooms 1 1.0440e+11 8.2231e+13 456680
## - total_rooms:median_income 1 1.3046e+11 8.2257e+13 456686
## - total_rooms:households 1 1.5955e+11 8.2286e+13 456694
## - total_rooms:population 1 1.7940e+11 8.2306e+13 456699
## - latitude:total_bedrooms 1 1.8561e+11 8.2312e+13 456700
## - longitude:total_rooms 1 2.0231e+11 8.2329e+13 456704
## - latitude:total_rooms 1 2.9682e+11 8.2423e+13 456728
## - population:households 1 2.9729e+11 8.2424e+13 456728
## - median_income:ocean_proximity 3 4.2540e+11 8.2552e+13 456740
## - total_bedrooms:households 1 3.8552e+11 8.2512e+13 456750
## - longitude:latitude 1 3.8593e+11 8.2513e+13 456750
## - total_rooms:ocean_proximity 3 4.8757e+11 8.2614e+13 456756
## - longitude:housing_median_age 1 4.6704e+11 8.2594e+13 456771
## - population:ocean_proximity 3 7.1419e+11 8.2841e+13 456813
## - latitude:housing_median_age 1 6.4266e+11 8.2769e+13 456815
## - longitude:median_income 1 7.1390e+11 8.2841e+13 456832
## - latitude:median_income 1 8.1651e+11 8.2943e+13 456858
## - housing_median_age:population 1 1.0090e+12 8.3136e+13 456906
## - latitude:ocean_proximity 3 1.2450e+12 8.3372e+13 456944
## - housing_median_age:households 1 1.3474e+12 8.3474e+13 456990
## - longitude:ocean_proximity 3 2.1964e+12 8.4323e+13 457178
##
## Step: AIC=456656.4
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:median_income +
## longitude:ocean_proximity + latitude:housing_median_age +
## latitude:total_rooms + latitude:total_bedrooms + latitude:population +
## latitude:households + latitude:median_income + latitude:ocean_proximity +
## housing_median_age:total_rooms + housing_median_age:population +
## housing_median_age:households + housing_median_age:median_income +
## housing_median_age:ocean_proximity + total_rooms:population +
## total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity +
## total_bedrooms:population + total_bedrooms:households + population:households +
## population:median_income + population:ocean_proximity + households:median_income +
## median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - total_bedrooms:population 1 1.9534e+10 8.2157e+13 456651
## - latitude:households 1 2.1573e+10 8.2159e+13 456652
## <none> 8.2137e+13 456656
## - population:median_income 1 8.4172e+10 8.2221e+13 456668
## - latitude:population 1 9.8545e+10 8.2236e+13 456671
## - households:median_income 1 1.0403e+11 8.2241e+13 456673
## - housing_median_age:ocean_proximity 3 1.8748e+11 8.2325e+13 456674
## - housing_median_age:median_income 1 1.0984e+11 8.2247e+13 456674
## - housing_median_age:total_rooms 1 1.1277e+11 8.2250e+13 456675
## - total_rooms:median_income 1 1.2353e+11 8.2261e+13 456677
## - total_rooms:households 1 1.6280e+11 8.2300e+13 456687
## - longitude:total_bedrooms 1 1.7721e+11 8.2314e+13 456691
## - total_rooms:population 1 1.8512e+11 8.2322e+13 456693
## - longitude:total_rooms 1 1.9234e+11 8.2330e+13 456695
## - latitude:total_bedrooms 1 2.5537e+11 8.2393e+13 456710
## - latitude:total_rooms 1 2.8851e+11 8.2426e+13 456719
## - median_income:ocean_proximity 3 4.2590e+11 8.2563e+13 456733
## - total_bedrooms:households 1 3.8589e+11 8.2523e+13 456743
## - longitude:latitude 1 3.9955e+11 8.2537e+13 456747
## - total_rooms:ocean_proximity 3 4.7908e+11 8.2616e+13 456747
## - population:households 1 4.0817e+11 8.2545e+13 456749
## - longitude:housing_median_age 1 4.6702e+11 8.2604e+13 456763
## - latitude:housing_median_age 1 6.4257e+11 8.2780e+13 456807
## - population:ocean_proximity 3 7.3062e+11 8.2868e+13 456809
## - longitude:median_income 1 7.0672e+11 8.2844e+13 456823
## - latitude:median_income 1 8.0895e+11 8.2946e+13 456849
## - housing_median_age:population 1 1.0220e+12 8.3159e+13 456902
## - latitude:ocean_proximity 3 1.2725e+12 8.3410e+13 456944
## - housing_median_age:households 1 1.4900e+12 8.3627e+13 457017
## - longitude:ocean_proximity 3 2.2268e+12 8.4364e+13 457179
##
## Step: AIC=456651.3
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:median_income +
## longitude:ocean_proximity + latitude:housing_median_age +
## latitude:total_rooms + latitude:total_bedrooms + latitude:population +
## latitude:households + latitude:median_income + latitude:ocean_proximity +
## housing_median_age:total_rooms + housing_median_age:population +
## housing_median_age:households + housing_median_age:median_income +
## housing_median_age:ocean_proximity + total_rooms:population +
## total_rooms:households + total_rooms:median_income + total_rooms:ocean_proximity +
## total_bedrooms:households + population:households + population:median_income +
## population:ocean_proximity + households:median_income + median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## - latitude:households 1 2.1726e+10 8.2178e+13 456647
## <none> 8.2157e+13 456651
## - latitude:population 1 1.1018e+11 8.2267e+13 456669
## - housing_median_age:median_income 1 1.1078e+11 8.2267e+13 456669
## - housing_median_age:ocean_proximity 3 1.9057e+11 8.2347e+13 456669
## - housing_median_age:total_rooms 1 1.1619e+11 8.2273e+13 456671
## - households:median_income 1 1.2251e+11 8.2279e+13 456672
## - total_rooms:median_income 1 1.2384e+11 8.2281e+13 456672
## - population:median_income 1 1.3242e+11 8.2289e+13 456675
## - longitude:total_bedrooms 1 1.7604e+11 8.2333e+13 456686
## - longitude:total_rooms 1 1.8986e+11 8.2347e+13 456689
## - total_rooms:households 1 1.9171e+11 8.2348e+13 456689
## - latitude:total_bedrooms 1 2.5534e+11 8.2412e+13 456705
## - total_rooms:population 1 2.6676e+11 8.2423e+13 456708
## - latitude:total_rooms 1 2.8390e+11 8.2441e+13 456713
## - median_income:ocean_proximity 3 4.2500e+11 8.2582e+13 456728
## - longitude:latitude 1 3.9509e+11 8.2552e+13 456740
## - total_rooms:ocean_proximity 3 4.7901e+11 8.2636e+13 456741
## - longitude:housing_median_age 1 4.6885e+11 8.2626e+13 456759
## - latitude:housing_median_age 1 6.4334e+11 8.2800e+13 456802
## - population:ocean_proximity 3 7.2775e+11 8.2884e+13 456804
## - population:households 1 6.7935e+11 8.2836e+13 456811
## - total_bedrooms:households 1 6.8621e+11 8.2843e+13 456813
## - longitude:median_income 1 7.0865e+11 8.2865e+13 456819
## - latitude:median_income 1 8.1094e+11 8.2968e+13 456844
## - housing_median_age:population 1 1.0106e+12 8.3167e+13 456894
## - latitude:ocean_proximity 3 1.2720e+12 8.3429e+13 456939
## - housing_median_age:households 1 1.4778e+12 8.3635e+13 457009
## - longitude:ocean_proximity 3 2.2223e+12 8.4379e+13 457172
##
## Step: AIC=456646.9
## median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:median_income +
## longitude:ocean_proximity + latitude:housing_median_age +
## latitude:total_rooms + latitude:total_bedrooms + latitude:population +
## latitude:median_income + latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:population + housing_median_age:households +
## housing_median_age:median_income + housing_median_age:ocean_proximity +
## total_rooms:population + total_rooms:households + total_rooms:median_income +
## total_rooms:ocean_proximity + total_bedrooms:households +
## population:households + population:median_income + population:ocean_proximity +
## households:median_income + median_income:ocean_proximity
##
## Df Sum of Sq RSS AIC
## <none> 8.2178e+13 456647
## - latitude:population 1 8.9938e+10 8.2268e+13 456659
## - housing_median_age:total_rooms 1 1.0965e+11 8.2288e+13 456664
## - housing_median_age:median_income 1 1.0979e+11 8.2288e+13 456664
## - housing_median_age:ocean_proximity 3 1.9301e+11 8.2371e+13 456665
## - total_rooms:median_income 1 1.1791e+11 8.2296e+13 456667
## - households:median_income 1 1.1897e+11 8.2297e+13 456667
## - population:median_income 1 1.2010e+11 8.2299e+13 456667
## - total_rooms:households 1 1.8960e+11 8.2368e+13 456684
## - longitude:total_bedrooms 1 1.9646e+11 8.2375e+13 456686
## - longitude:total_rooms 1 2.0465e+11 8.2383e+13 456688
## - total_rooms:population 1 2.7003e+11 8.2448e+13 456705
## - latitude:total_rooms 1 3.0622e+11 8.2485e+13 456714
## - median_income:ocean_proximity 3 4.3223e+11 8.2611e+13 456725
## - latitude:total_bedrooms 1 4.0071e+11 8.2579e+13 456737
## - longitude:latitude 1 4.1726e+11 8.2596e+13 456741
## - total_rooms:ocean_proximity 3 5.0035e+11 8.2679e+13 456742
## - longitude:housing_median_age 1 4.7676e+11 8.2655e+13 456756
## - latitude:housing_median_age 1 6.5598e+11 8.2834e+13 456801
## - total_bedrooms:households 1 6.7859e+11 8.2857e+13 456807
## - population:households 1 6.8453e+11 8.2863e+13 456808
## - population:ocean_proximity 3 7.7513e+11 8.2954e+13 456811
## - longitude:median_income 1 7.1905e+11 8.2897e+13 456817
## - latitude:median_income 1 8.2539e+11 8.3004e+13 456843
## - housing_median_age:population 1 9.9965e+11 8.3178e+13 456886
## - latitude:ocean_proximity 3 1.2632e+12 8.3442e+13 456932
## - housing_median_age:households 1 1.4589e+12 8.3637e+13 457000
## - longitude:ocean_proximity 3 2.2125e+12 8.4391e+13 457165
summary(back_bic_mod)
##
## Call:
## lm(formula = median_house_value ~ longitude + latitude + housing_median_age +
## total_rooms + total_bedrooms + population + households +
## median_income + ocean_proximity + longitude:latitude + longitude:housing_median_age +
## longitude:total_rooms + longitude:total_bedrooms + longitude:median_income +
## longitude:ocean_proximity + latitude:housing_median_age +
## latitude:total_rooms + latitude:total_bedrooms + latitude:population +
## latitude:median_income + latitude:ocean_proximity + housing_median_age:total_rooms +
## housing_median_age:population + housing_median_age:households +
## housing_median_age:median_income + housing_median_age:ocean_proximity +
## total_rooms:population + total_rooms:households + total_rooms:median_income +
## total_rooms:ocean_proximity + total_bedrooms:households +
## population:households + population:median_income + population:ocean_proximity +
## households:median_income + median_income:ocean_proximity,
## data = temp_housing_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -471806 -36852 -8923 25350 616260
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) -7.296e+06 9.152e+05 -7.972
## longitude -5.241e+04 8.032e+03 -6.525
## latitude 2.929e+05 2.736e+04 10.705
## housing_median_age -7.643e+04 7.648e+03 -9.993
## total_rooms 6.752e+02 1.077e+02 6.267
## total_bedrooms -2.750e+03 5.218e+02 -5.271
## population -1.033e+02 1.829e+01 -5.651
## households -1.830e+02 1.618e+01 -11.309
## median_income -7.382e+05 6.002e+04 -12.300
## ocean_proximityINLAND 7.288e+05 2.479e+05 2.939
## ocean_proximityNEAR BAY -2.423e+07 1.239e+06 -19.561
## ocean_proximityNEAR OCEAN -7.422e+05 3.102e+05 -2.392
## longitude:latitude 2.179e+03 2.131e+02 10.223
## longitude:housing_median_age -9.658e+02 8.838e+01 -10.928
## longitude:total_rooms 8.930e+00 1.247e+00 7.160
## longitude:total_bedrooms -4.255e+01 6.066e+00 -7.015
## longitude:median_income -9.513e+03 7.088e+02 -13.420
## longitude:ocean_proximityINLAND 1.116e+04 2.949e+03 3.785
## longitude:ocean_proximityNEAR BAY -2.384e+05 1.092e+04 -21.835
## longitude:ocean_proximityNEAR OCEAN -5.991e+03 3.701e+03 -1.619
## latitude:housing_median_age -1.114e+03 8.688e+01 -12.818
## latitude:total_rooms 1.101e+01 1.257e+00 8.758
## latitude:total_bedrooms -6.141e+01 6.130e+00 -10.019
## latitude:population 2.513e+00 5.294e-01 4.746
## latitude:median_income -1.053e+04 7.320e+02 -14.379
## latitude:ocean_proximityINLAND 1.381e+04 3.079e+03 4.485
## latitude:ocean_proximityNEAR BAY -1.298e+05 8.441e+03 -15.372
## latitude:ocean_proximityNEAR OCEAN 1.057e+02 3.864e+03 0.027
## housing_median_age:total_rooms -3.385e-01 6.459e-02 -5.241
## housing_median_age:population -1.488e+00 9.405e-02 -15.824
## housing_median_age:households 7.216e+00 3.775e-01 19.116
## housing_median_age:median_income 1.218e+02 2.322e+01 5.244
## housing_median_age:ocean_proximityINLAND 9.414e+02 1.453e+02 6.479
## housing_median_age:ocean_proximityNEAR BAY -9.824e+01 1.608e+02 -0.611
## housing_median_age:ocean_proximityNEAR OCEAN 2.189e+02 1.324e+02 1.653
## total_rooms:population -3.332e-03 4.051e-04 -8.224
## total_rooms:households 8.135e-03 1.180e-03 6.891
## total_rooms:median_income 1.553e+00 2.857e-01 5.435
## total_rooms:ocean_proximityINLAND -1.346e+01 1.331e+00 -10.113
## total_rooms:ocean_proximityNEAR BAY 6.043e+00 2.412e+00 2.505
## total_rooms:ocean_proximityNEAR OCEAN -2.618e+00 1.491e+00 -1.756
## total_bedrooms:households -6.688e-02 5.130e-03 -13.037
## population:households 2.742e-02 2.094e-03 13.094
## population:median_income -3.624e+00 6.607e-01 -5.485
## population:ocean_proximityINLAND 2.963e+01 2.360e+00 12.553
## population:ocean_proximityNEAR BAY -1.362e+01 4.772e+00 -2.854
## population:ocean_proximityNEAR OCEAN 8.383e+00 2.852e+00 2.939
## households:median_income 1.382e+01 2.532e+00 5.459
## median_income:ocean_proximityINLAND 1.019e+04 1.058e+03 9.633
## median_income:ocean_proximityNEAR BAY 2.301e+03 1.031e+03 2.232
## median_income:ocean_proximityNEAR OCEAN 3.432e+03 8.250e+02 4.160
## Pr(>|t|)
## (Intercept) 1.64e-15 ***
## longitude 6.95e-11 ***
## latitude < 2e-16 ***
## housing_median_age < 2e-16 ***
## total_rooms 3.75e-10 ***
## total_bedrooms 1.37e-07 ***
## population 1.62e-08 ***
## households < 2e-16 ***
## median_income < 2e-16 ***
## ocean_proximityINLAND 0.003292 **
## ocean_proximityNEAR BAY < 2e-16 ***
## ocean_proximityNEAR OCEAN 0.016756 *
## longitude:latitude < 2e-16 ***
## longitude:housing_median_age < 2e-16 ***
## longitude:total_rooms 8.36e-13 ***
## longitude:total_bedrooms 2.37e-12 ***
## longitude:median_income < 2e-16 ***
## longitude:ocean_proximityINLAND 0.000154 ***
## longitude:ocean_proximityNEAR BAY < 2e-16 ***
## longitude:ocean_proximityNEAR OCEAN 0.105494
## latitude:housing_median_age < 2e-16 ***
## latitude:total_rooms < 2e-16 ***
## latitude:total_bedrooms < 2e-16 ***
## latitude:population 2.09e-06 ***
## latitude:median_income < 2e-16 ***
## latitude:ocean_proximityINLAND 7.31e-06 ***
## latitude:ocean_proximityNEAR BAY < 2e-16 ***
## latitude:ocean_proximityNEAR OCEAN 0.978167
## housing_median_age:total_rooms 1.61e-07 ***
## housing_median_age:population < 2e-16 ***
## housing_median_age:households < 2e-16 ***
## housing_median_age:median_income 1.59e-07 ***
## housing_median_age:ocean_proximityINLAND 9.43e-11 ***
## housing_median_age:ocean_proximityNEAR BAY 0.541162
## housing_median_age:ocean_proximityNEAR OCEAN 0.098260 .
## total_rooms:population < 2e-16 ***
## total_rooms:households 5.69e-12 ***
## total_rooms:median_income 5.55e-08 ***
## total_rooms:ocean_proximityINLAND < 2e-16 ***
## total_rooms:ocean_proximityNEAR BAY 0.012240 *
## total_rooms:ocean_proximityNEAR OCEAN 0.079153 .
## total_bedrooms:households < 2e-16 ***
## population:households < 2e-16 ***
## population:median_income 4.19e-08 ***
## population:ocean_proximityINLAND < 2e-16 ***
## population:ocean_proximityNEAR BAY 0.004322 **
## population:ocean_proximityNEAR OCEAN 0.003292 **
## households:median_income 4.85e-08 ***
## median_income:ocean_proximityINLAND < 2e-16 ***
## median_income:ocean_proximityNEAR BAY 0.025656 *
## median_income:ocean_proximityNEAR OCEAN 3.19e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 63190 on 20584 degrees of freedom
## Multiple R-squared: 0.7008, Adjusted R-squared: 0.7001
## F-statistic: 964.2 on 50 and 20584 DF, p-value: < 2.2e-16